Geometric Series Worksheet
Understand and apply the concepts of geometric series, including finding the common ratio, sum of finite geometric series, and sum of infinite geometric series.
Includes
Standards
Topics
Geometric Series
Name:
Date:
Score:
Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. Which of the following is a geometric series?
2, 4, 6, 8, ...
1, 3, 5, 7, ...
3, 6, 12, 24, ...
10, 8, 6, 4, ...
2. What is the common ratio of the sequence 5, 10, 20, 40, ...?
2
5
10
1/2
3. In a geometric series, each term after the first is found by multiplying the previous one by a fixed, non-zero number called the .
4. The sum of an infinite geometric series converges if the absolute value of the common ratio is than 1.
5. Find the sum of the first 5 terms of the geometric series 3, 9, 27, ...
6. The series 1 + 1/2 + 1/4 + 1/8 + ... is a converging geometric series.
True
False
7. An initial investment of $1000 grows by 5% each year. Write the first 4 terms of the sequence representing the investment value at the end of each year. Is this a geometric series? Explain why.
Match the formula with its description.
1. Sn = a(1 - r^n) / (1 - r)
a. Sum of an infinite geometric series
2. S = a / (1 - r)
b. Sum of a finite geometric series